change_ring broken on polynomials

[Vincent Delecroix]

If the polynomial can be coerced in the new base ring, the result of change_ring is a constant

sage: p = ZZ['x']([1,2,3])
sage: p.change_ring(QQ['x']).degree()
0
sage: p.change_ring(SR).degree()
0

[Nils Bruin]

Note that change_ring is supposed to change the base ring. For instance, we have:

sage: p.change_ring(QQ['y']).degree()
2
sage: p.change_ring(QQ['y']).parent()
Univariate Polynomial Ring in x over Univariate Polynomial Ring in y over Rational Field

In your case, you basically end up with

sage: QQ['x']['x'](p)
3*x^2 + 2*x + 1

and as it goes with coercion, the x of p coerces as low in the tower as possible.

Perhaps you'd prefer the result

sage: QQ['x']['x'](p)
3*x^2 + 2*x + 1

There's some work to be done, though:

sage: R.<x,y>=ZZ[]
sage: f=x^2+y^2
sage: f.change_ring(QQ['x','y']).monomials()
[1]
sage: f.change_ring(QQ['x']).monomials()
[x^2, y^2]
sage: f.change_ring(QQ['y']).monomials()
[x^2, y^2]

which does match

sage: QQ['x']['x','y'](f).monomials()
[x^2, y^2]
sage: QQ['x','y']['x','y'](f).monomials()
[1]

but doesn't seem to fit the pattern of "coerce 'x' as low as possible. But then, following that rule consistently might not be such a good idea.

sage: QQ['x']['x'](QQ['x']['x'].0).degree()
1

[Vincent Delecroix]

I think that change_ring on elements should uniformly be

def change_ring(self, R):
    return self.parent().change_ring(R)(list(self))

I don't plan to change anything to the _element_constructor_ which is definitely allowed to behave differently.

[Vincent Delecroix]

New commits:

​319bb43

fix change_ring for polynomials

[Julian Rüth]

Changes look good to me. nbruin, do you agree?

[Ralf Stephan]

Patchbot is green, too.

[Vincent Delecroix]

ping

[Julian Rüth]

Since nbruin has not reacted, let's assume that he does at least not strongly disagree…